Solve for $x$ : $ 2|x + 3| + 10 = -2|x + 3| + 7 $
Explanation: Add $ {2|x + 3|} $ to both sides: $ \begin{eqnarray} 2|x + 3| + 10 &=& -2|x + 3| + 7 \\ \\ { + 2|x + 3|} && { + 2|x + 3|} \\ \\ 4|x + 3| + 10 &=& 7 \end{eqnarray} $ Subtract ${10}$ from both sides: $ \begin{eqnarray} 4|x + 3| + 10 &=& 7 \\ \\ { - 10} &=& { - 10} \\ \\ 4|x + 3| &=& -3 \end{eqnarray} $ Divide both sides by ${4}$ $ \dfrac{4|x + 3|} {{4}} = \dfrac{-3} {{4}} $ Simplify: $ |x + 3| = -\dfrac{3}{4}$ The absolute value cannot be negative. Therefore, there is no solution.